Order in metallic chains. II. Coupled chains

The possibility of long-range order in a quasi-one-dimensional metal is studied from the standpoint of the two existing exactly soluble models of the interacting electron gas in one dimension. The presence of interchain low-momentum-transfer electron-electron interactions does not give rise to a phase transition of any type but serves only to renormalize the effective intrachain interactions. In the region of the space of intrachain interactions for which the purely one-dimensional charge-density wave response function is divergent as $T\to 0$, the presence of nearest-neighbor interchain large-momentum-transfer electron-electron scattering gives rise to a phase transition only of the charge-density-wave type. When the electronic motion is not restricted to one spatial dimension, phase transitions of either the singlet superconducting or charge-density-wave type may occur, depending upon the effective intrachain interactions. These phase transitions are investigated in the "mean-field" and "self-avoiding random-walk" approximations, and the effects of fluctuations in the interchain couplings are found to be small.